Quantitative relation between intermolecular and intramolecular binding of pro-rich peptides to SH3 domains

Flexible linkers are often found to tether binding sequence motifs or connect protein domains. Here we analyze three usages of flexible linkers: 1), intramolecular binding of proline-rich peptides (PRPs) to SH3 domains for kinase regulation; 2), intramolecular binding of PRP for increasing the folding stability of SH3 domains; and 3), covalent linking of PRPs and other ligands for high-affinity bivalent binding. The basis of these analyses is a quantitative relation between intermolecular and intramolecular binding constants. This relation has the form K(i) = K(e0)p for intramolecular binding and K(e) = K(e01)K(e02)p for bivalent binding. The effective concentration p depends on the length of the linker and the distance between the linker attachment points in the bound state. Several applications illustrate the usefulness of the quantitative relation. These include intramolecular binding to the Itk SH3 domain by an internal PRP and to a circular permutant of the alpha-spectrin SH3 domain by a designed PRP, and bivalent binding to the two SH3 domains of Grb2 by two linked PRPs. These and other examples suggest that flexible linkers and sequence motifs tethered to them, like folded protein domains, are also subject to tight control during evolution.